Method of predicting and minimizing model OPC deviation due to mix/match of exposure tools using a calibrated Eigen decomposition model

ABSTRACT

A method for generating models for simulating the imaging performance of a plurality of exposure tools. The method includes the steps of: generating a calibrated model for a first exposure tool capable of estimating an image to be produced by the first exposure tool for a given photolithography process, where the calibrated model includes a first set of basis functions; generating a model of a second exposure tool capable of estimating an image to be produced by the second exposure tool for the photolithography process, where the model includes a second set of basis functions; and representing the second set of basis functions as a linear combination of the first set of basis functions so as to generate an equivalent model function corresponding to the second exposure tool, where the equivalent model function produces a simulated image corresponding to the image generated by the second exposure tool for the photolithography process.

This application claims the benefit of provisional application60/539,997, filed on Jan. 30, 2004 and titled Method Of Predicting AndMinimizing Model OPC Deviation Due To Mix/Match Of Exposure Tools UsingA Calibrated Eigen Decomposition Model, which is herein incorporated byreference in its entirety.

TECHNICAL FIELD OF THE INVENTION

The field of the invention relates generally to a method, apparatus andprogram for utilizing models to simulate the aerial image resulting froma target mask pattern imaged by a given process, and more particularlyrelates to a method, apparatus and program product for allowing a model,which is calibrated utilizing a first exposure tool, to be utilized topredict the imaging results of a second exposure tool without having torecalibrate the model.

BACKGROUND OF THE INVENTION

Lithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In such a case, the mask may contain acircuit pattern corresponding to an individual layer of the IC, and thispattern can be imaged onto a target portion (e.g. comprising one or moredies) on a substrate (silicon wafer) that has been coated with a layerof radiation-sensitive material (resist). In general, a single waferwill contain a whole network of adjacent target portions that aresuccessively irradiated via the projection system, one at a time. In onetype of lithographic projection apparatus, each target portion isirradiated by exposing the entire mask pattern onto the target portionin one go; such an apparatus is commonly referred to as a wafer stepper.In an alternative apparatus, commonly referred to as a step-and-scanapparatus, each target portion is irradiated by progressively scanningthe mask pattern under the projection beam in a given referencedirection (the “scanning” direction) while synchronously scanning thesubstrate table parallel or anti-parallel to this direction. Since, ingeneral, the projection system will have a magnification factor M(generally <1), the speed V at which the substrate table is scanned willbe a factor M times that at which the mask table is scanned. Moreinformation with regard to lithographic devices as described herein canbe gleaned, for example, from U.S. Pat. No. 6,046,792, incorporatedherein by reference.

In a manufacturing process using a lithographic projection apparatus, amask pattern is imaged onto a substrate that is at least partiallycovered by a layer of radiation-sensitive material (resist). Prior tothis imaging step, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures, such as a post-exposure bake(PEB), development, a hard bake and measurement/inspection of the imagedfeatures. This array of procedures is used as a basis to pattern anindividual layer of a device, e.g., an IC. Such a patterned layer maythen undergo various processes such as etching, ion-implantation(doping), metallization, oxidation, chemo-mechanical polishing, etc.,all intended to finish off an individual layer. If several layers arerequired, then the whole procedure, or a variant thereof, will have tobe repeated for each new layer. Eventually, an array of devices will bepresent on the substrate (wafer). These devices are then separated fromone another by a technique such as dicing or sawing, whence theindividual devices can be mounted on a carrier, connected to pins, etc.

For the sake of simplicity, the projection system may hereinafter bereferred to as the “lens”; however, this term should be broadlyinterpreted as encompassing various types of projection systems,including refractive optics, reflective optics, and catadioptricsystems, for example. The radiation system may also include componentsoperating according to any of these design types for directing, shapingor controlling the projection beam of radiation, and such components mayalso be referred to below, collectively or singularly, as a “lens”.Further, the lithographic apparatus may be of a type having two or moresubstrate tables (and/or two or more mask tables). In such “multiplestage” devices the additional tables may be used in parallel, orpreparatory steps may be carried out on one or more tables while one ormore other tables are being used for exposures. Twin stage lithographicapparatus are described, for example, in U.S. Pat. No. 5,969,441,incorporated herein by reference.

The photolithographic masks referred to above comprise geometricpatterns corresponding to the circuit components to be integrated onto asilicon wafer. The patterns used to create such masks are generatedutilizing CAD (computer-aided design) programs, this process often beingreferred to as EDA (electronic design automation). Most CAD programsfollow a set of predetermined design rules in order to create functionalmasks. These rules are set by processing and design limitations. Forexample, design rules define the space tolerance between circuit devices(such as gates, capacitors, etc.) or interconnect lines, so as to ensurethat the circuit devices or lines do not interact with one another in anundesirable way. The design rule limitations are typically referred toas “critical dimensions” (CD). A critical dimension of a circuit can bedefined as the smallest width of a line or hole or the smallest spacebetween two lines or two holes. Thus, the CD determines the overall sizeand density of the designed circuit.

Of course, one of the goals in integrated circuit fabrication is tofaithfully reproduce the original circuit design on the wafer (via themask). As is known, optical proximity correction (OPC) features may beincorporated into the mask design to enhance the resulting image suchthat it more accurately represents the target pattern. Further, it isalso known to utilize models of the desired process to simulate theaerial image of a given target pattern. Such models allow the operatorto review the effects of adjusting masking features and OPC features onthe resulting image without having to actually image a wafer, therebysaving both significant cost and time in the design process. One suchmodeling method is described in U.S. patent application Ser. No.10/981,750, filed on Nov. 5, 2004, which is hereby incorporated byreference in its entirety.

Another goal in photolithography is to be able to utilize the same“process” for imaging a given pattern with different lithography systems(e.g., scanners) without having to expend considerable amounts of timeand resources determining the necessary settings of each lithographysystem to achieve optimal/acceptable imaging performance. As is known,designers/engineers spend a considerable amount of time and moneydetermining the optimal settings of a lithography system, which includenumerical aperture (NA), σ_(in), σ_(out), etc., when initially settingup a given process to work with a particular scanner so that theresulting image satisfies the design requirements and process robustnessrequirements. Indeed, finding an optimal photolithography processcondition for each layer involves enormous effort from the engineeringside trough simulations and experiments. A method for allowing a givenprocess to be utilized with different lithography systems is disclosedin U.S. patent application Ser. No. 10/926,400 filed on Aug. 26, 2004,which is hereby incorporated by reference herein in its entirety.

As noted above, target patterns are typically subjected to a simulationprocess using a calibrated model of the photolithography process so asto allow the designer to optimize the mask pattern such that theresulting image matches the target pattern within a defined tolerance.The model used in such data manipulation, which is commonly referred asto model OPC, is typically calibrated on a specific exposure tool underspecific exposure conditions. However, as noted above, it is notuncommon for a photolithography process to be exported onto otherexposure tools of the same class, in order to satisfy the high volumeproduction requirements in a manufacturing environment. As such, it ishighly desirable to be able to utilize the model calibrated on a firstexposure tool on another exposure tool, without having to performanother complete calibration process, which is both expensive and timeconsuming. Currently, there is no known method for allowing a modelcalibrated on a first exposure tool to be utilized with another exposuretool without performing a complete calibration process on the otherexposure tool.

SUMMARY OF THE INVENTION

It is an object of the present invention to address the foregoingdeficiency in the prior art. To summarize, the present invention relatesto a method and apparatus that allows a model calibrated on a firstexposure tool to be utilized to generate a second model for simulatingthe imaging performance of a second exposure tool, without having toperform a calibration process for the second model utilizing the secondexposure tool.

More specifically, the present invention relates to a method forgenerating models for simulating the imaging performance of a pluralityof exposure tools. The method includes the steps of: generating acalibrated model for a first exposure tool capable of estimating animage to be produced by the first exposure tool for a givenphotolithography process, where the calibrated model includes a firstset of basis functions; generating a model of a second exposure toolcapable of estimating an image to be produced by the second exposuretool for the photolithography process, where the model includes a secondset of basis functions; and representing the second set of basisfunctions as a linear combination of the first set of basis functions soas to generate an equivalent model function corresponding to the secondexposure tool, where the equivalent model function produces a simulatedimage corresponding to the image generated by the second exposure toolfor the photolithography process.

The present invention provides significant advantages over prior artmethods. Most importantly, the present invention is very cost effectiveas it allows a previously calibrated model to be utilized in conjunctionwith other exposure tools without having to perform a calibrationprocess on the other exposure tools.

Another advantage of the present invention is that by using a calibratedmodel which has been modified for use with the other exposure tools, itis possible to perform testing/simulation of the entire chip, as opposedto only limited testing which would be the case if direct experimentaltests were conducted on the other exposure tools.

Additional advantages of the present invention will become apparent tothose skilled in the art from the following detailed description ofexemplary embodiments of the present invention.

Although specific reference may be made in this text to the use of theinvention in the manufacture of ICs, it should be explicitly understoodthat the invention has many other possible applications. For example, itmay be employed in the manufacture of integrated optical systems,guidance and detection patterns for magnetic domain memories,liquid-crystal display panels, thin-film magnetic heads, etc. Theskilled artisan will appreciate that, in the context of such alternativeapplications, any use of the terms “reticle”, “wafer” or “die” in thistext should be considered as being replaced by the more general terms“mask”, “substrate” and “target portion”, respectively.

In the present document, the terms “radiation” and “beam” are used toencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) andEUV (extreme ultra-violet radiation, e.g. having a wavelength in therange 5–20 nm).

The term mask as employed in this text may be broadly interpreted asreferring to generic patterning means that can be used to endow anincoming radiation beam with a patterned cross-section, corresponding toa pattern that is to be created in a target portion of the substrate;the term “light valve” can also be used in this context. Besides theclassic mask (transmissive or reflective; binary, phase-shifting,hybrid, etc.), examples of other such patterning means include:

-   a programmable mirror array. An example of such a device is a    matrix-addressable surface having a viscoelastic control layer and a    reflective surface. The basic principle behind such an apparatus is    that (for example) addressed areas of the reflective surface reflect    incident light as diffracted light, whereas unaddressed areas    reflect incident light as undiffracted light. Using an appropriate    filter, the said undiffracted light can be filtered out of the    reflected beam, leaving only the diffracted light behind; in this    manner, the beam becomes patterned according to the addressing    pattern of the matrix-addressable surface. The required matrix    addressing can be performed using suitable electronic means. More    information on such mirror arrays can be gleaned, for example, from    U.S. Pat. No. 5,296,891 and U.S. Pat. No. 5,523,193, which are    incorporated herein by reference.-   a programmable LCD array. An example of such a construction is given    in U.S. Pat. No. 5,229,872, which is incorporated herein by    reference.

The invention itself, together with further objects and advantages, canbe better understood by reference to the following detailed descriptionand the accompanying schematic drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthe specification, together with the description serve to explain theprinciples of the invention. In the drawings:

FIG. 1 is an exemplary flowchart illustrating the method of the presentinvention.

FIG. 2 illustrates an exemplary process for minimizing the mismatchbetween exposure tools being utilized to implement the samephotolithography process.

FIG. 3 illustrates an exemplary eigen decomposition model (e.g., a firstorder eigen decomposition model).

FIG. 4 illustrates an exemplary process for generating a calibratedeigen decomposition model.

FIG. 5 illustrates an exemplary processing system for implementing thepresent invention.

FIG. 6 schematically depicts a lithographic projection apparatussuitable for use with a mask designed with the aid of the currentinvention.

DETAILED DESCRIPTION OF THE INVENTION

Disclosed herein is a method and apparatus for allowing a model, whichis calibrated in conjunction with a first exposure tool and is capableof simulating the imaging performance of the first exposure tool, to beutilized to generate a second model capable of simulating the imagingperformance of a second exposure tool without having to perform acalibration of the second model and second exposure tool. It is notedthat the exemplary method detailed below utilizes an eigen functiondecomposition model (referred to as an Eigen Decomposition Model, orEDM), for modeling the performance of the imaging process. However, itis also possible to utilize the methods of the present invention withother types of models.

Prior to discussing the method of the present invention, a briefdiscussion regarding the generation of an eigen decomposition model ispresented. A more detailed description of the generation of the eigendecomposition model can be found in U.S. patent application Ser. No.10/981,750 filed on Nov. 5, 2004, as noted above.

As noted, in the following example illustrating the method of thepresent invention, a constant threshold eigen decomposition model isutilized. A constant threshold eigen decomposition model is premised onseveral fundamental theorems. The first is that any 2D binary image canbe obtained by cutting a band limited real valued function at a constantthreshold. The second is that the aerial image from an optical imagesystem is a band limited function, and therefore, the effective degreesof freedom of the aerial image are finite. The third is that the optimalbasis functions for describing the aerial image are the eigen functions,which can be solved utilizing an integral equation whose operator isdetermined by the optical image system setting.

Under partial coherent illumination conditions that are typically usedin semiconductor manufacturing, the optical imaging system itself isnonlinear in character. The aerial image, i.e. the light intensitydistribution at the image plane, from any given mask pattern, can bereadily calculated rather accurately using well-known formulas inoptics, see for example, H. H. Hopkins, Proc. Roy. Soc., A, 217 (1953),408, herein incorporated by reference. The response of chemicallyamplified resist to light intensity and the subsequent resistdevelopment in solvent are all very nonlinear. The final developedpattern on a wafer can be viewed as binary, either with resist orwithout resist on top of the wafer substrate. The main function of themodel is to provide a mathematical formula that can predict the binaryimage on the wafer from the mask pattern or the aerial image accurately.Stated mathematically,T(x,y)=F(M(x,y))  (1)where T(x,y) is the produced binary image on the wafer, and M(x,y) isthe input pattern on the mask (which can include OPC features). Frepresents the unknown functional form, which is the core of any model.In the simplest constant threshold model, the binary image is achievedby cutting the aerial image of M(x,y) using a constant threshold. It isnoted that the binary image obtained by cutting the aerial image at aconstant threshold does not typically fully agree with the experimentalresult due to the finiteness of the resist contrast. The simplicity inobtaining the binary image using a constant threshold, however, is veryattractive. There exists a mathematical theorem which states any binaryfunction T(x,y), whose value is either 0 or 1, can be obtained bythresholding a band-limited continuous function F(x,y) to any specifiedaccuracy. The higher the required accuracy, the larger the requiredbandwidth of the function F(x,y). Such a continuous function F(x,y) istermed a system pseudo intensity function (SPIF) in the model of thepresent invention.

In other words, in the eigen decomposition model the object is toidentify a transformation function that relates the aerial image toanother band limited non-negative real valued function from which adesired binary image can be achieved by thresholding the non-negativereal value function at certain value. The new band limited non-negativereal valued function is referred to as a system pseudo intensityfunction (SPIF).

The transformation from the aerial image I(x,y), which can be readilycalculated, to SPIF constitutes a key element in the model. The value ofSPIF at location (x,y) depends not only on the value of aerial imageintensity at (x,y), but also on all the values of the aerial imageintensity around point (x,y). Mathematically, the SPIF can be expressedas:SPIF(x,y)=G(I(x,y))  (2).

Due to the complicated nature of the photolithography process, it isunlikely to derive an exact functional form of G based on first physicalprinciples. As such, an approximate functional form of G is utilized.This is possible only if the aerial image I(x,y) has finite effectivedegrees of freedom, which is true according to Shanon's samplingtheorem, since the aerial image I(x,y) is a band-limited function, asdiscussed in C. E. Shannon, Proc. IRE, 37, (1946), 429, hereinincorporated by reference.

This transformation is not a point-to-point transformation. In otherwords, as stated above, the SPIF value at (x,y) is not only dependent onthe aerial image value at (x,y), but also all values of the aerial imagearound (x,y). It becomes apparent that a method of describing the aerialimage intensity distribution around (x,y) is required. It turns out thatthe effective degrees of freedom of the aerial image is finite accordingto Shannon's sample theorem, as discussed in C. E. Shannon, Proc. IRE,37, (1946), 429, herein incorporated by reference, since the aerialimage is a band limited function.

It has also been proven that there exists an optimal set of basisfunctions to decompose the aerial image that is produced from an opticalimaging system at a specific imaging setting. In other words, the aerialimage is calculated by the convolution of the mask function M(x,y) withthe eigen functions. More particularly, with an orthonormal set offunctions {φ_(i)}, the aerial image can be calculated using thefollowing equation:

$\begin{matrix}{{I( {x,y} )} = {\sum\limits_{i = 1}^{\infty}{\alpha_{i}{{\phi_{i} \otimes M}}^{2}}}} & (3)\end{matrix}$where {φ_(i)} constitute a complete set of orthonormal functions,{α_(i)} are the corresponding weight factors, {circle around (×)}represents the convolution operation between the orthonormal function{φ_(i)} and the mask transmission function M. In the language of imagingtheory, equation (3) shows that a partially coherent imaging system canbe decomposed into a series of coherent imaging systems. Although thereare other methods to decompose a partially coherent imaging system intoa series of coherent imaging systems, the method described above hasbeen proven to be an optimal one, often called optimal coherentdecomposition. See, for example, Y. C. Pati and T. Kailath, J. Opt. Soc.Am. A 11, (1994), 2438, herein incorporated by reference.

Continuing, both {φ_(i)} and {α_(i)} can be obtained by solving thefollowing integral equation,∫∫W(x ₁ ′, y ₁ ′; x ₂ ′, y ₂′)φ_(i)(x ₂ ′, y ₂′)dx ₂ ′dy ₂′=α_(i)φ_(i)(x₁ ′, y ₁′)  (4)andW(x ₁ ′, y ₁ ′; x ₂ ′, y ₂′)=γ(x ₂ ′−x ₁ ′, y ₂ ′−y ₁′)K(x ₁ ′, y₁′)K*(x ₂ ′, y ₂′)  (5)where γ(x₂′−x₁′, y₂′−y₁′) is the mutual coherence between (x₁′, y₁′) and(x₂′, y₂′) at the object plane, which is determined by illumination, andK(x₁′, y₁′) is the impulse response function of the optical imagingsystem, which is determined by the pupil function of the optical system.More specifically, it is the complex amplitude at the point (x₁′, y₁′)in the image plane, due to a disturbance of unit amplitude and zerophase at (0, 0) in the object plane.

Under the illumination conditions commonly employed in semiconductormanufacturing, {α_(i)} drops rapidly with its index (i.e., α₁≧α₂≧α₃≧ . .. ≧α_(N) . . . , and usually when N around 7, the (α_(N) is very small,close to zero), and only few terms are necessary to approximate theaerial image accurately. The contributions from other terms can bedisregarded in the presence of noise that typically exists in a realoptical imaging process. With this observation, one can assume only thefirst N terms are important, and equation (3) becomes:

$\begin{matrix}{{I( {x,y} )} = {\sum\limits_{i = 1}^{i = N}{\alpha_{i}{{\phi_{i} \otimes M}}^{2}}}} & (6)\end{matrix}$If one defines:S _(i)=α_(i)|φ_(i) {circle around (×)}M| ²  (7)It then becomes evident that the SPIF value at (x,y) must solely dependon the values of S₁, S₂, . . . , S_(N), and equation (1) becomes:SPIF(x,y)=G(S₁ , S ₂ , . . . , S _(N))  (8)Using successive expansion, one has:

$\begin{matrix}{{{SPIF}( {x,y} )} = {{G( {0,0,\ldots\mspace{11mu},0} )} + {\sum\limits_{i = 1}^{i = N}{\beta_{i}S_{i}}} + {\sum\limits_{i = 1}^{i = N}{\sum\limits_{j = 1}^{j = N}{\eta_{ij}S_{i}S_{j}}}} + \ldots}} & (9)\end{matrix}$If all the S_(i) terms are zero (i=1, 2, . . . , N), SPIF should bezero, and therefore, G(0,0, . . . , 0) should be zero. Morespecifically, when all S terms equal zero, SPIF=G(0,0,0, . . .) from(9). However, only when a mask is completely dark can all S terms equalto zero. In this case, SPIF is obviously equal to zero. As such,equation (10) can be obtained from equation (9). Equation (10) expresseshow SPIF (x,y) is related to the signals Si at (x,y).

$\begin{matrix}{{{SPIF}( {x,y} )} = {{\sum\limits_{i = 1}^{i = N}{\beta_{i}S_{i}}} + {\sum\limits_{i = 1}^{i = N}{\sum\limits_{j = 1}^{j = N}{\eta_{ij}S_{i}S_{j}}}} + \ldots}} & (10)\end{matrix}$

{β_(i)} and {η_(ij)} are the model parameters that characterize theresist response to the signals {S₁, S₂, . . . , S_(N)}. It should beunderstood that {β_(i)} and {η_(ij)} are independent of the opticalimaging setting, as these parameters depend only on the processfollowing the exposure. As such, {β_(i)} and {η_(ij)} can be readilyobtained by calibrating the model equation (10) with experimental data.

Utilizing the constant threshold eigen decomposition model describedabove, it is possible to develop the method that allows for predictingthe photolithography performance for exposure tools other than theexposure tool utilized to calibrate the model.

More specifically, assuming the exposure tool used for calibrating themodel is exposure tool A, and the optimal set of basis functions forexposure tool A is {φ^(A) _(i)}. Also assuming that exposure tool B'soptimal set of basis functions is {φ^(B) _(n)}. The set of basisfunctions {φ^(B) _(n)} can be different from the set of basis functions{φ^(A) _(i)} either due to slight difference in illuminator profile orsome difference in aberration characteristics between the two exposuretools. However, because both {φ^(B) _(n)} and {φ^(A) _(i)} are completesets of basis functions, and both possess the same bandwidth, eachfunction in {φ^(B) _(n)} can be expressed as a linear combination of{φ^(A) _(i)}. More specifically:

$\begin{matrix}{{\phi_{n}^{B} = {\sum\limits_{i = 1}^{\infty}{\chi_{i}^{n}\phi_{i}^{A}}}}{{where}\text{:}}} & (11) \\{\chi_{i}^{n} = {\int{\int{{\phi_{n}^{B} \cdot \phi_{i}^{A*}}{\mathbb{d}x}{\mathbb{d}y}}}}} & (12)\end{matrix}$

In typical applications, only the first M functions in {φ^(B) _(n)} andthe first N functions in {φ^(A) _(i)} are significant in terms ofweighting factor. As such, it is only necessary to consider theamplitudes of the projected signals from {S^(B) _(n),n=1,2, . . . M}onto {S^(A) _(i), i=1,2, . . . , N}. More specifically:

$\begin{matrix}\begin{matrix}{S_{n}^{B} = {\alpha_{n}^{B}{{\phi_{n}^{B} \otimes M}}^{2}}} \\{= {{\alpha_{n}^{B}( {\sum\limits_{i = 1}{\chi_{i}^{n}{\phi_{i}^{A} \otimes M}}} )}( {\sum\limits_{t = 1}{\chi_{t}^{n}{\phi_{t}^{A} \otimes M}}} )^{*}}} \\{= {{\alpha_{n}^{B}{\sum\limits_{i = 1}{{\chi_{i}^{n}}^{2}{{\phi_{i}^{A} \otimes M}}^{2}}}} +}} \\{\alpha_{n}^{B}{\sum\limits_{i \neq t}{{\chi_{i}^{n}( \chi_{t}^{n} )}^{*}( {\phi_{i}^{A} \otimes M} )( {\phi_{t}^{A} \otimes M} )^{*}}}} \\{= {\frac{\alpha_{n}^{B}}{\alpha_{i}^{A}}{\sum\limits_{i = 1}{{\chi_{i}^{n}}^{2}S_{i}}}}}\end{matrix} & (13)\end{matrix}$

The second term vanishes in equation (13), because of the lack of phasecorrelation between fields from (φ^(A) _(i){circle around (×)}M) and(φ^(A) _(t){circle around (×)}M)* when i≠t, and the time averaged valuetherefore becomes null. From equation (13), the projected signals inrepresentation of {φ^(A) _(i)} are:

$\begin{matrix}{{{\sum\limits_{n = 1}^{n = M}{\frac{\alpha_{n}^{B}}{\alpha_{i}^{A}}{\chi_{i}^{n}}^{2}S_{i}}};{i = 1}},2,\ldots\mspace{11mu},N} & (14)\end{matrix}$The equivalent SPIF is:

$\begin{matrix}{{{SPIF}( {x,y} )} = {{\sum\limits_{i = 1}^{i = N}{\beta_{i}( {\sum\limits_{n = 1}^{n = M}{\frac{\alpha_{n}^{B}}{\alpha_{i}^{A}}{\chi_{i}^{n}}^{2}S_{i}}} )}} + {\sum\limits_{i = 1}^{i = N}{\sum\limits_{j = 1}^{j = N}{{\eta_{ij}( {\sum\limits_{n = 1}^{n = M}{\frac{\alpha_{n}^{B}}{\alpha_{i}^{A}}{\chi_{i}^{n}}^{2}S_{i}}} )}( {\sum\limits_{n = 1}^{n = M}{\frac{\alpha_{n}^{B}}{\alpha_{j}^{A}}{\chi_{j}^{n}}^{2}S_{j}}} )}}} + \ldots}} & (15)\end{matrix}$Using the same threshold, the binary images from exposure tool B can bereadily obtained from the SPIF expressed in equation (15).

FIG. 1 is a flowchart illustrating the foregoing method for utilizing amodel calibrated for a first exposure tool to predict the imagingperformance of another exposure tool. Referring to FIG. 1, in the firststep of the process, Step 10, the photolithography process to beutilized is defined. Next, in Step 12, a set of kernels (i.e., themodel) defining the first exposure tool (i.e., exposure tool A) and thephotolithography process is generated. In the given embodiment, as notedabove, an eigen decomposition model is utilized.

Thereafter, in Step 14, a plurality of test structures are subjected toan actual imaging process utilizing exposure tool A and thephotolithography process utilized to generate the set of kernels. InStep 16, the model is calibrated. This is accomplished by inputting thetest structures into the model and then comparing the results of themodel to the actual imaging results produced in Step 14. The model isthen adjusted until the imaging results produced by the model match theactual imaging results within a predetermined error tolerance. As wouldbe known by those of skill in the art, the predetermined error tolerancewill vary in accordance with the specific application andphotolithography tools being utilized. Once the model is tuned so as tobe within the predefined error tolerance, the model is deemedcalibrated.

Next, in Step 18, a set of kernels (i.e., the second model) defining thesecond exposure tool (i.e., exposure tool B) and the photolithographyprocess is generated. It is noted that the illuminator profile andaberration of exposure tool B are considered when generating the kernelsdefining exposure tool B, as these are the dominant factors with regardto variations in performance between the two exposure tools. Of course,however, other factors can be considered, such as, but not limited tofocus settings. It is noted that it is possible to measure theilluminator and aberration associated with exposure tool B in order todetermine the values of these factors prior to generating the set ofkernels associated with exposure tool B. This can be accomplished, forexample, by using a metrology tool on the scanners/steppers.

In the next step, Step S20, the set of kernels for exposure tool Bgenerated in Step S18 are expressed as a linear combination of the setof kernels for exposure tool A and an equivalent SPIF function isgenerated in accordance with equations 14 and 15. In other words, theaerial images from exposure tool B can be represented using its owncharacteristic kernels, however, the response of the resist to suchsignal representation is unknown. The resist response is known only whensignals are represented in exposure tool A's characteristic kernels,because a process or model calibration has been performed for exposuretool A. It is this reason that the signals from exposure tool B need tobe converted into signals that are represented in exposure tool A'skernels. Next, in Step S22, the SPIF function generated in Step S20 canbe utilized to generate binary images corresponding to the imagingresults that would be produced by exposure tool B, if exposure tool Bwhere utilized to image a mask pattern.

Thus, the present invention allows a first model calibrated inconjunction with a first exposure tool to be utilized to generate asecond model for simulating the imaging performance of a second exposuretool, without having to perform a calibration process on the secondmodel.

In addition to the allowing photolithography printing performanceprediction on exposure tools that are not calibrated in the mannerdiscussed above, the present invention also provides a method forminimizing the mismatch between different exposure tools which are beingutilized to perform the same photolithography process. The minimizationof mismatch between exposure tools has become an ever increasing problemand pressing issue in low k1 photolithography, particularly for thosetechnologies in which mask data corrections are required using acalibrated photolithography model. The minimization of mismatch betweenexposure tools can both reduce the effective cost of masks and increasethe productivity significantly. It is noted that exposure tool mismatchresults dominantly from variations in the illuminator profiles andaberrations between the different exposure tools. As long as thepredominate basis for variations in exposure tool performance can bediagnosed and determined, for example, such as aberrations, the presentinvention provides a method for reducing such variations.

FIG. 2 illustrates an exemplary process for minimizing the mismatchbetween exposure tools being utilized to implement the same process inaccordance with the present invention. The following example assumesthat there are a cluster of exposure tools of the same class, {A, B, C,. . . }, and that exposure tool A is the master tool on which aparticular photolithography process has been calibrated and aphotolithography model has been developed. The first step, S40, is toidentify the master tool, which in this example, is exposure tool A. Thenext step, S42, is to measure the dominant factors on exposure tool A,which contribute to variations in imaging performance between the tools.These factors include, but are not limited to, the illuminator profileand aberrations. Thereafter, in Step S44, a set of kernels (i.e., themodel) defining exposure tool A and the photolithography process isgenerated. In the given embodiment, as discussed above, an eigendecomposition model is utilized. In Step S46, a plurality of teststructures are subjected to an actual imaging process utilizing exposuretool A and the selected photolithography process to obtain actualimaging results. Then, in Step S48, the imaging results generated by themodel produced in Step S44 are compared to the actual imaging resultsproduced in Step S46, and the results of the comparison are utilized togenerate a database indicating the difference between the modelperformance of exposure tool A and the actual performance of exposuretool A. Then, by adjusting the parameters, for example, {β^(A)i} ofequation (9), the error between the modeled results and the experimentscan be minimized. This step, Step 48, is basically the model calibrationprocess for exposure tool A.

As explained below, only the model defined by {β^(A)i} will be utilizedin predicting the imaging performance on other exposure tools. It isnoted that the experimental results from exposure tool A are onlyutilized in calibrating the model for exposure tool A. After the modelon exposure tool A is calibrated, the experimental results from exposuretool A are no longer required. It is noted that this portion of theprocess is similar to that described above in conjunction with FIG. 1.

The next step, Step S50, is to select one of the other exposure tools,for example, exposure tool B, and measure the same dominant factors forexposure tool B, Step 52, that were measured for exposure tool A in StepS42. Then, in the same manner as Step S44, a set of kernels (i.e., themodel) defining exposure tool B and the photolithography process isgenerated, Step S54. In the given embodiment, as noted above, an eigendecomposition model is utilized.

Next, returning to step, S44, the set of kernels for exposure tool Bgenerated in Step S54 are expressed as a linear combination of the setof kernels for exposure tool A. Thereafter, returning to Step 48, theimaging performance for exposure tool B is determined utilizing the SPIFfunction of equation 15 for any structures, including but not limited tothe test structures utilized in Step S46 to generate actual imagingresults.

Once the imaging results for exposure tool B are determined, in Step 56,these results are compared to imaging results generated by the model forexposure tool A to determine the differences in imaging performancebetween the exposure tools. If the difference between the imagingperformance (i.e., mismatch) of exposure tool A and exposure tool B iswithin a predetermined error tolerance, Step 58, the process iscompleted, Step 60, and exposure tool B is deemed capable of imaging thedesired target mask pattern.

However, if the difference in imaging results is not within thepredefined error tolerance, the process proceeds to Step 62, in whichadjustments are made to the exposure tool in an effort to minimize thevariations or mismatch in the imaging performance between exposure toolB and the master exposure tool A. For example, the engineer or operatorcan adjust the optical elements on the machine to modify the illuminatorprofiles or aberration characteristics. Once the adjustments are made,Steps S52, S54, S44, S48, S56 and S58 are repeated to confirm that theadjusted exposure tool is within the predefined error tolerance.

FIGS. 3 and 4 illustrate a more detailed explanation of the modelcalibration process referred to in FIG. 1. Referring to FIGS. 3 and 4,an input 2 containing characteristics of the mask pattern is provided toan optical imaging model 4, step S100. Eigen functions and eigen valuesrepresenting the imaging process are determined from characteristics ofthe illumination source and imaging process to be utilized including,for example, the numerical aperture NA and the wavelength λ, step S102.The characteristics of test mask (i.e., the test structures) are used todetermine a mask function M(x,y), step S104, which is provided as input2. The aerial image is determined by convoluting the eigen functionswith the mask function M(x,y), step S105. A first order eigen functionindicative of the resist effect 6 may be utilized in determining theaerial image to account for the effect a particular resist has on theactual aerial image. A predetermined constant threshold is applied tothe aerial image to generate an initial SPIF with predicted contours,step S106. The predicted contours are compared to known contours of thetest mask, which are determined by actually printing the test mask imageusing the same illumination conditions and process, step S110. If thepredicted contours are within a predetermined error tolerance of themeasured contours, step S112 YES (it is noted that in the preferredembodiment, 2-dimensional counters are utilized in the comparisonprocess), then the predictive model is certified as being an accuratemodel and the model calibration is complete, step S114. If the predictedcontours are not within a predetermined error tolerance, step S112 NO,then the weight of each term associated with each eigen function, whichdefine the imaging process, is adjusted, step S116 and a new SPIF isproduced. Then, a the constant threshold is applied to the new SPIF,step S108, and the process in steps S108–116 is repeated until a modelis produced which provides contours within the predetermined errortolerance.

FIG. 5 illustrates an exemplary processing system for implementing theeigen decomposition models illustrated in FIGS. 1–4. As illustrated inFIG. 5, an exemplary mask optimization unit may contain a processor 1000which receives input from an input 1003. Processor 1000 may be aconventional microprocessor or may be a specially designed processingunit, such as an EEPROM or EPROM or a fabricated integrated circuit.Input 1003 may be any type of electronic input device, such as akeyboard or a mouse, or may be a memory or internet connection.Processor 1000 preferably retrieves stored protocols from ROM 1002 andRAM 1001, such as protocols to implement the processing illustrated inFIGS. 1–4, and stores information on RAM 1001. The calculated results ofprocessor 1000 may be displayed on display 1004 and may be provided to amask fabrication unit.

FIG. 6 schematically depicts a lithographic projection apparatussuitable for use with a mask designed with the aid of the currentinvention. The apparatus comprises:

-   a radiation system Ex, IL, for supplying a projection beam PB of    radiation. In this particular case, the radiation system also    comprises a radiation source LA;-   a first object table (mask table) MT provided with a mask holder for    holding a mask MA (e.g., a reticle), and connected to first    positioning means for accurately positioning the mask with respect    to item PL;-   a second object table (substrate table) WT provided with a substrate    holder for holding a substrate W (e.g., a resist-coated silicon    wafer), and connected to second positioning means for accurately    positioning the substrate with respect to item PL;-   a projection system (“lens”) PL (e.g., a refractive, catoptric or    catadioptric optical system) for imaging an irradiated portion of    the mask MA onto a target portion C (e.g., comprising one or more    dies) of the substrate W.

As depicted herein, the apparatus is of a transmissive type (i.e., has atransmissive mask). However, in general, it may also be of a reflectivetype, for example (with a reflective mask). Alternatively, the apparatusmay employ another kind of patterning means as an alternative to the useof a mask; examples include a programmable mirror array or LCD matrix.

The source LA (e.g., a mercury lamp or excimer laser) produces a beam ofradiation. This beam is fed into an illumination system (illuminator)IL, either directly or after having traversed conditioning means, suchas a beam expander Ex, for example. The illuminator IL may compriseadjusting means AM for setting the outer and/or inner radial extent(commonly referred to as σ-outer and σ-inner, respectively) of theintensity distribution in the beam. In addition, it will generallycomprise various other components, such as an integrator IN and acondenser CO. In this way, the beam PB impinging on the mask MA has adesired uniformity and intensity distribution in its cross-section.

It should be noted with regard to FIG. 6 that the source LA may bewithin the housing of the lithographic projection apparatus (as is oftenthe case when the source LA is a mercury lamp, for example), but that itmay also be remote from the lithographic projection apparatus, theradiation beam that it produces being led into the apparatus (e.g., withthe aid of suitable directing mirrors); this latter scenario is oftenthe case when the source LA is an excimer laser (e.g., based on KrF, ArFor F₂ lasing). The current invention encompasses at least both of thesescenarios.

The beam PB subsequently intercepts the mask MA, which is held on a masktable MT. Having traversed the mask MA, the beam PB passes through thelens PL, which focuses the beam PB onto a target portion C of thesubstrate W. With the aid of the second positioning means (andinterferometric measuring means IF), the substrate table WT can be movedaccurately, e.g. so as to position different target portions C in thepath of the beam PB. Similarly, the first positioning means can be usedto accurately position the mask MA with respect to the path of the beamPB, e.g., after mechanical retrieval of the mask MA from a mask library,or during a scan. In general, movement of the object tables MT, WT willbe realized with the aid of a long-stroke module (coarse positioning)and a short-stroke module (fine positioning), which are not explicitlydepicted in FIG. 6. However, in the case of a wafer stepper (as opposedto a step-and-scan tool) the mask table MT may just be connected to ashort stroke actuator, or may be fixed.

The depicted tool can be used in two different modes:

-   In step mode, the mask table MT is kept essentially stationary, and    an entire mask image is projected in one go (i.e., a single “flash”)    onto a target portion C. The substrate table WT is then shifted in    the x and/or y directions so that a different target portion C can    be irradiated by the beam PB;-   In scan mode, essentially the same scenario applies, except that a    given target portion C is not exposed in a single “flash”. Instead,    the mask table MT is movable in a given direction (the so-called    “scan direction”, e.g., the y direction) with a speed v, so that the    projection beam PB is caused to scan over a mask image;    concurrently, the substrate table WT is simultaneously moved in the    same or opposite direction at a speed V=Mv, in which M is the    magnification of the lens PL (typically, M=¼ or ⅕). In this manner,    a relatively large target portion C can be exposed, without having    to compromise on resolution.

The concepts disclosed herein may simulate or mathematically model anygeneric imaging system for imaging sub wavelength features, and may beespecially useful with emerging imaging technologies capable ofproducing wavelengths of an increasingly smaller size. Emergingtechnologies already in use include EUV (extreme ultra violet)lithography that is capable of producing a 193 nm wavelength with theuse of a ArF laser, and even a 157 nm wavelength with the use of aFluorine laser. Moreover, EUV lithography is capable of producingwavelengths within a range of 20–5 nm by using a synchrotron or byhitting a material (either solid or a plasma) with high energy electronsin order to produce photons within this range. Because most materialsare absorptive within this range, illumination may be produced byreflective mirrors with a multi-stack of Molybdenum and Silicon. Themulti-stack mirror has a 40 layer pairs of Molybdenum and Silicon wherethe thickness of each layer is a quarter wavelength. Even smallerwavelengths may be produced with X-ray lithography. Typically, asynchrotron is used to produce an X-ray wavelength. Since most materialis absorptive at x-ray wavelengths, a thin piece of absorbing materialdefines where features would print (positive resist) or not print(negative resist).

While the concepts disclosed herein may be used for imaging on asubstrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

Software functionalities of the processor 1000 involve programming,including executable code, are used to implement the above describedmethod of determining optimal DOE for different lithography systems. Thesoftware code is executable by the general-purpose computer. Inoperation, the code and possibly the associated data records are storedwithin a general-purpose computer platform. At other times, however, thesoftware may be stored at other locations and/or transported for loadinginto the appropriate general-purpose computer systems. Hence, theembodiments discussed above involve one or more software products in theform of one or more modules of code carried by at least onemachine-readable medium. Execution of such code by a processor of thecomputer system enables the platform to implement the catalog and/orsoftware downloading functions, in essentially the manner performed inthe embodiments discussed and illustrated herein.

As used herein, terms such as computer or machine “readable medium”refer to any medium that participates in providing instructions to aprocessor for execution. Such a medium may take many forms, includingbut not limited to, non-volatile media, volatile media, and transmissionmedia. Non-volatile media include, for example, optical or magneticdisks, such as any of the storage devices in any computer(s) operatingas one of the server platform, discussed above. Volatile media includedynamic memory, such as main memory of such a computer platform.Physical transmission media include coaxial cables; copper wire andfiber optics, including the wires that comprise a bus within a computersystem. Carrier-wave transmission media can take the form of electric orelectromagnetic signals, or acoustic or light waves such as thosegenerated during radio frequency (RF) and infrared (IR) datacommunications. Common forms of computer-readable media thereforeinclude, for example: a floppy disk, a flexible disk, hard disk,magnetic tape, any other magnetic medium, a CD-ROM, DVD, any otheroptical medium, less commonly used media such as punch cards, papertape, any other physical medium with patterns of holes, a RAM, a PROM,and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrierwave transporting data or instructions, cables or links transportingsuch a carrier wave, or any other medium from which a computer can readprogramming code and/or data. Many of these forms of computer readablemedia may be involved in carrying one or more sequences of one or moreinstructions to a processor for execution.

It is also noted that variations of the foregoing embodiments of thepresent invention are also possible. As already mentioned, while theembodiments disclosed above illustrate the present invention beingutilized in conjunction with an eigen decomposition model, it can alsobe utilized with other types of model simulators.

Although the present invention has been described and illustrated indetail, it is to be clearly understood that the same is by way ofillustration and example only and is not to be taken by way oflimitation, the scope of the present invention being limited only by theterms of the appended claims.

1. A method for generating models for simulating the imaging performanceof a plurality of exposure tools, said method comprising the steps of:generating a calibrated model for a first exposure tool, said calibratedmodel capable of estimating an image to be produced by said firstexposure tool for a given photolithography process, said calibratedmodel comprising a first set of basis functions; generating a model of asecond exposure tool, said model capable of estimating an image to beproduced by said second exposure tool for said photolithography process,said model comprising a second set of basis functions; and representingsaid second set of basis functions as a linear combination of said firstset of basis functions so as to generate an equivalent model functioncorresponding to said second exposure tool, wherein said equivalentmodel function produces a simulated image corresponding to the imagegenerated by said second exposure tool for said photolithographyprocess.
 2. The method of claim 1, wherein said calibrated model isgenerated by: defining parameters of said first exposure tool andprocessing conditions to be utilized in said photolithography process;generating an initial model of said first exposure tool; defining aplurality of test structures; imaging the test structures utilizing saidfirst exposure tool and processing conditions of said photolithographyprocess to obtain actual imaging results; generating simulated imagingresults by subjecting said test structures to said initial model;comparing said simulated imaging results to said actual imaging results;and adjusting said initial model such that the difference between saidsimulated imaging results and said actual imaging results is less than apredefined criteria, wherein said adjusted initial model corresponds tosaid calibrated model.
 3. The method of claim 1, wherein said first setof basis functions and said second set of basis functions comprise aplurality of eigen functions.
 4. The method of claim 1, wherein there isno calibration process performed on said second exposure tool.
 5. Themethod of claim 2, wherein said comparing said simulated imaging resultsto said actual imaging results utilizes two-dimensional contour patternsin the comparison process.
 6. A computer readable medium having storedthereon a computer program having executable code, wherein execution ofthe code by at least one programmable computer causes the at least oneprogrammable computer to perform a sequence of steps for generatingmodels for simulating the imaging performance of a plurality of exposuretools, said sequence of steps comprising: generating a calibrated modelfor a first exposure tool, said calibrated model capable of estimatingan image to be produced by said first exposure tool for a givenphotolithography process, said calibrated model comprising a first setof basis functions; generating a model of a second exposure tool, saidmodel capable of estimating an image to be produced by said secondexposure tool for said photolithography process, said model comprising asecond set of basis functions; and representing said second set of basisfunctions as a linear combination of said first set of basis functionsso as to generate an equivalent model function corresponding to saidsecond exposure tool, wherein said equivalent model function produces asimulated image corresponding to the image generated by said secondexposure tool for said photolithography process.
 7. The computerreadable medium of claim 6, wherein said step of generating saidcalibrated model comprises the steps of: defining parameters of saidfirst exposure tool and processing conditions to be utilized in saidphotolithography process; generating an initial model of said firstexposure tool; defining a plurality of test structures; imaging the teststructures utilizing said first exposure tool and processing conditionsof said photolithography process to obtain actual imaging results;generating simulated imaging results by subjecting said test structuresto said initial model; comparing said simulated imaging results to saidactual imaging results; and adjusting said initial model such that thedifference between said simulated imaging results and said actualimaging results is less than a predefined criteria, wherein saidadjusted initial model corresponds to said calibrated model.
 8. Thecomputer readable medium of claim 6, wherein said first set of basisfunctions and said second set of basis functions comprise a plurality ofeigen functions.
 9. The computer readable medium of claim 6, whereinthere is no calibration process performed on said second exposure tool.10. The computer readable medium of claim 7, wherein said comparing saidsimulated imaging results to said actual imaging results utilizestwo-dimensional contour patterns in the comparison process.
 11. Anapparatus for generating models for simulating the imaging performanceof a plurality of exposure tools, said apparatus comprising: means forgenerating a calibrated model for a first exposure tool, said calibratedmodel capable of estimating an image to be produced by said firstexposure tool for a given photolithography process, said calibratedmodel comprising a first set of basis functions; means for generating amodel of a second exposure tool, said model capable of estimating animage to be produced by said second exposure tool for saidphotolithography process, said model comprising a second set of basisfunctions; and means for representing said second set of basis functionsas a linear combination of said first set of basis functions so as togenerate an equivalent model function corresponding to said secondexposure tool, wherein said equivalent model function produces asimulated image corresponding to the image generated by said secondexposure tool for said photolithography process.
 12. The apparatus ofclaim 11, wherein said means for generating said calibrated modelcomprises: means for defining parameters of said first exposure tool andprocessing conditions to be utilized in said photolithography process;means for generating an initial model of said first exposure tool; meansfor defining a plurality of test structures; means for imaging the teststructures utilizing said first exposure tool and processing conditionsof said photolithography process to obtain actual imaging results; meansfor generating simulated imaging results by subjecting said teststructures to said initial model; means for comparing said simulatedimaging results to said actual imaging results; and means for adjustingsaid initial model such that the difference between said simulatedimaging results and said actual imaging results is less than apredefined criteria, wherein said adjusted initial model corresponds tosaid calibrated model.
 13. The apparatus of claim 11, wherein said firstset of basis functions and said second set of basis functions comprise aplurality of eigen functions.
 14. The apparatus of claim 11, whereinthere is no calibration process performed on said second exposure tool.15. The apparatus of claim 12, wherein said comparing said simulatedimaging results to said actual imaging results utilizes two-dimensionalcontour patterns in the comparison process.